## Duke Mathematical Journal

### Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions

#### Abstract

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation $iu_t + \Delta u = |u|^{4/n} u$ for large, spherically symmetric, $L^2_x({\mathbb R}^n)$ initial data in dimensions $n\geq 3$. After using the concentration-compactness reductions in [32] to reduce to eliminating blow-up solutions that are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to [10], [23], [36]) in order to conclude the argument

#### Article information

Source
Duke Math. J., Volume 140, Number 1 (2007), 165-202.

Dates
First available in Project Euclid: 25 September 2007

https://projecteuclid.org/euclid.dmj/1190730777

Digital Object Identifier
doi:10.1215/S0012-7094-07-14015-8

Mathematical Reviews number (MathSciNet)
MR2355070

Zentralblatt MATH identifier
1187.35246

#### Citation

Tao, Terence; Visan, Monica; Zhang, Xiaoyi. Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions. Duke Math. J. 140 (2007), no. 1, 165--202. doi:10.1215/S0012-7094-07-14015-8. https://projecteuclid.org/euclid.dmj/1190730777

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